Method for determining the equivalency index of goods, processes, and services

ABSTRACT

A method is disclosed wherewith a person skilled in the art of statistical quality control may determine whether a process, goods, or service is statistically equivalent to another of known quality, or to a desired target quality. The method may also be used to determine whether multiplicities of goods, processes, or services are statistically equivalent to one another and of a desired quality. The method makes the determination based on an equivalency index that is derived from integration of the probability distribution of data of measurement taken from products associated with the process, goods or services.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] This invention is related to field of statistical quality controland more specifically related to a method of determining an equivalencyindex of goods, processes and services.

[0003] 2. Description of the Related Art

[0004] Every goods, process and service possess a number of parametersthat jointly describe what the user thinks of as quality. Theseparameters are often called quality characteristics. Qualitycharacteristics may be physical such as length, weight, voltage, andviscosity, or sensory such as taste, appearance, color, and ease of use,or time orientation such as reliability, and durability.

[0005] In the past, the buyers had to carry the burden of examining,judging, and testing goods for themselves. Competition in the marketplace has shifted the burden to the producers. The producers not onlymust screen out the non-conforming products before they reach thecustomers, they must continuously monitor their manufacturing processesfor continuous quality improvement in order to compete.

[0006] To aid such endeavor, statistical tools have been developed.Today, it is common for the producers of goods such as automobile,computer, clothing, and its field service and provider of services suchas generation and distribution of electrical energy, Internet services,telephone services, public transportation, banking, health, andaccounting to adopt statistical quality control tools in their routinebusiness and manufacturing operation. Such tools have becomeindispensable in their endeavor to compete for market share.

[0007] Among the tools that are prevalent among the practitioners ofstatistical quality control are the control chart, the Pareto diagram,the scatter plot, the histogram, the experimental design, and theacceptance sampling.

[0008] One common character of these tools is that they are mosteffective when used to correlate between characteristic qualityparameters of a product, be it goods or service, and the input orprocess parameters that can affect the quality parameters. Practitionersuse these tools to compare the variation of the quality parameters tothe predetermined limits and to distinguish between common and specialcauses so as to understand and analyze the variation in the quality of agoods or service. Once the causes are identified, the informationenables the practitioner to make necessary modification in order tocontrol the effect and reduce the variation. These tools, however, havea common shortcoming.

[0009] In today's business environment, producers may be manufacturingtheir goods in many production sites, often in distant parts of theworld. Service providers may also provide their products in many diversegeographical locations. Yet, the goods and service must be controlled tothe same quality standard. A customer will expect the same quality offood and service from a restaurant in Tokyo, Japan as he receives inQuadalajara, Mexico if the restaurants bear the same name. Amicro-controller chip maker in Taiwan who tries to qualify as a supplierto a German company must demonstrate that its chips meet the customer'sspecification and are equal, statistically speaking, to the parts thecustomer currently uses. The traditional statistical quality controlmethods and tools are less helpful for such purposes. When the issueconcerns the degree of equivalency among a multiplicity of items ofgoods, processes, and services, it is difficult, with such tools, toreach an unambiguous conclusion readily and to express the conclusion asa concise numerical format.

BRIEF SUMMARY OF THE INVENTION

[0010] It is the object of this invention to provide a method with whicha person of ordinary skill in the area of statistical quality controlcan determine whether a goods, process, or service is statisticallyequivalent to another of known quality.

[0011] It is also the object of this invention to provide a method withwhich a person of ordinary skill in the area of statistical qualitycontrol can determine whether a goods, process, or service isstatistically equivalent to a required standard.

[0012] It is also the object of this invention to provide a method withwhich a person of ordinary skill in the area of statistical qualitycontrol can determine whether a multiplicity of goods, processes, orservices are statistically equivalent to one another and of a desiredquality.

[0013] Examples of such occasion are abundant: an owner or operator of aplant may need to judge the quality of a potential electricity supplierin terms of fluctuation of the supply voltage over time and compare thatto the current supplier, an electronic system maker may need to judgethe quality equivalency of the printed circuit board from a new vendorsin terms of the thickness variation of the board in view of hisproduction equipment specifications, other examples are the fill volumeof soft drink beverage from various bottling machines, the net weight ofa dry leach product from multiple production lines, the tensile strengthof alternative new alloy materials for an automotive engine part, thetime to failure of an electronic component from different vendors, orthe results of many quality-control technicians measuring the surfacefinish of a metal parts.

BRIEF DESCRIPTION OF THE DRAWINGS

[0014]FIG. 1 depicts the steps of a method for declaring a process intwo semiconductor IC fabrication facilities A and B (FABs A and B) to beequivalent in quality based on equivalency indices.

[0015]FIG. 2 depicts the steps of a method for declaring a process in asemiconductor IC fabrication facility as being equivalent in quality toa baseline process based on equivalency indices.

[0016]FIG. 3 depicts the steps of a method for declaring a plurality ofsemiconductor IC fabrication facilities as being equivalent in qualitybased on equivalency indices.

[0017]FIG. 4 depicts two probability distribution curves. One curve isgenerated from measurements taken from products of a semiconductor ICfabrication facility. FABs A the other curve is from PAB B.

[0018]FIG. 5 depicts the passing and failing thresholds on anequivalency index scale and the corresponding scale measuring theseparation between two probability distributions.

[0019]FIG. 6 depicts two probability distribution curves. the othercurve is a baseline facility LAB L.

[0020]FIG. 7 depicts three probability distribution curves. One curve isgenerated from measurements taken from products of a semiconductor ICfabrication facility. FABs A, the second curve is from FAB B and thethird curve is from FAB C. Also depicted is the target value T of theparameter.

DETAILED DESCRIPTION OF THE INVENTION

[0021]FIG. 1 depicts a specific example of the first embodiment of thisinvention, a method with which a semiconductor manufacturer maydetermine whether two of its integrated circuit (IC) manufacturingfacilities (FABs) produce an IC product that is statisticallyequivalent. The two FABs may or may not have identical type and model ofmanufacturing equipment, they may or may not share identical recipe ofmanufacturing process. Although the method is illustrated withsemiconductor IC product, this method can easily apply to other type ofproducts. This method is also not limited to manufactured goods but caneasily apply to services. What is required is a set of identifiable,measurable parameters that jointly describe what the user thinks of asquality of the product. A person skilled in the art of statisticalquality control would be able to adopt this method to his or her ownsituation with equal effectiveness, regardless of which type of goods orservice is being produced. This principle also applies to the otherembodiment of this invention.

[0022] In step 101, the method requires one to identify one or morevariable parameters that are characteristic of the IC manufacturingprocess, that can be measured from a product manufactured with theprocess. The number of parameters that are necessary to make thisequivalency determination may be large or small, depending on thecomplexity of the process and the economy of the operation. In modemsemiconductor integrated circuit products, one may choose amongparameters related to a typical transistor in the integrated circuit,such as the transistor channel length, the gate oxide thickness, thedrive current, gate to substrate leakage current etc.

[0023] In step 102, one takes measurements of an identified parameter instep 101, for instance, the transistor drive current from a group of ICproducts manufactured in a first facility, FAB A. The measurement mayrequire hand probing by an operator if the desired sample size is small.

[0024] Otherwise, it may require an automated system that incorporatesautomated testing system for data acquisition and computer system fordata crunching.

[0025] In step 103, one records the data from the measurements. Again,depending on the sample size, the recording may be in a laboratorynotebook, a personal computer, or a fully automated system.

[0026] In step 104, one constructs a probability distribution curve fromthe data recorded in step 103. Element 401 of FIG. 4 depicts such adistribution curve. Depending on the nature of the parameter, the datamay form different types of distribution. The most common distributionis the normal distribution or the bell-curve distribution. Other typesof distribution encountered in a typical manufacturing process includebinomial, chi-square, t, F, exponential, gamma, Pascal, Poisson andWeibull distribution. The method described here works well with normaland other types of discrete and continuous distributions. In case thedistribution does not conform to a commonly recognizable model, a personskilled in the art of statistical quality control will be able to usenumerical method or graphical method in implementing the teachingdisclosed in this invention.

[0027] In step 105, one extracts the average and the standard deviationfrom the probability distribution. The extraction may be accomplishedmanually or by a computer. It is familiar to a person skilled in the artof statistical quality control.

[0028] In step 106, 107, 108, and 109, one repeats the procedure ofmeasurement and extraction on a group of products manufactured in asecond facility, FAB B. FIG. 4, element 402 depicts a probabilitydistribution curve from FAB B.

[0029] With the two curves showing in the same drawing, one can readilyobserve qualitatively the overlapping of the probability distribution.The more the two curves overlap, the more similar the products from ofthe two facilities are. The degree of the overlap of the curves,therefore, serves as a good indication of the equivalency of the twoprocesses under comparison. The remaining of the method quantifies theequivalency by performing an integration of the probabilitydistributions over a proper range.

[0030] In step 110, one chooses the range limits of the integration. Inthis example, the chosen limits are the three-sigma points of the twocurves. The concept of three-sigma is familiar to a person skilled instatistical quality control. The upper limit of the integration ischosen to be the lesser of the two three-sigma points that are the upperlimit of 99.7% inclusion of all data points under the curves. The lowerlimit is the greater of the two three sigma points that are the lowerlimit of 99.7% inclusion of all data point under the two curves. In FIG.4, the upper and lower limits are designated as D, element 412, and C,411 respectively.

[0031] In step 111, one carries out the integration of the sum of thetwo probability distribution functions. When the two distributions arenormal distribution, the result of the integration lies between 2×99.7%and 2×0.3%. In a mathematical form the integration may be written as$E_{PAB} = {{\left( {\frac{1}{2}{\int_{C}^{D}{\left\lbrack {{f_{A}(x)} + {f_{B}(x)}} \right\rbrack \quad {x}}}} \right)/99.7}\%}$

[0032] where E_(PAB) is the equivalency index of the parameter P of FABsA and B, D is element 412 in FIG. 4, the upper three-sigma point ofelement 402, C is element 411 in FIG. 4, the lower three-sigma point ofelement 401, f_(A)(x) is the probability distribution function of datafrom FAB A, element 401 in FIG. 4, f_(B)(x) is the probabilitydistribution function of data from FAB B, element 402 in FIG. 4.

[0033] In step 112, a division by a weighing factor of 2×99.7%normalizes the result of the integration to yield a number between 100%and less than 1%. The purpose of the normalization is for the ease ofautomation. Choice of other weighing factors is also possible.Otherwise, the normalization may also be omitted.

[0034] In step 114, this number is defined as the equivalency index ofthe parameter under test.

[0035] In step 115, one sets the thresholds to delineate the ranges ofpassing and failing of an equivalent index. In this example, passing isset at 98% and failing is set at 90%. These particular threshold valuesare chosen because according to the current semiconductor industrypractice, when two probability curves plotting data generated form twogroups of products, are within one sigma shift distant apart, the twogroups of products are considered as not statistically significantlydifferent from each other. If, however, the distance is more than atwo-sigma shift, the two groups are considered to be significantlydifferent. The threshold value of 98%, as shown in FIG. 5, convenientlycorresponds to a one-sigma shift and the value of 90% is very closelycorresponding to a two-sigma shift between the two probabilitydistribution curves.

[0036] While there is a statistical base for choosing these thresholdvalues, the method disclosed in this invention is equally effective withother choice of the threshold values based on other considerations suchas custom or economy. Also, this step may be performed temporallyindependent of other steps in the method. If the some considerationapplies for all the identified parameters under consideration, the sameset of threshold values may be used. Otherwise, one may choose to usedifferent threshold values for different parameters.

[0037]FIG. 5 depicts the relationship between values of an equivalencyindex and the corresponding shift of two probability distribution curvesthat generate the equivalency index. Element 501 depicts the scale ofequivalency indices and element 502 depicts the scale of thecorresponding shift.

[0038] In step 116, one compares the equivalency index E_(PAB) to theranges set in step 115. If E_(PAB) is in the range above the upperthreshold value of 98%, the passing range or a green zone, one woulddeclare that FABs A and B are equivalent in quality with respect toparameter P. On the other hand, if E_(PAB) is in the range below thelower threshold value of 90%, a failing range or a red zone, one woulddeclare that FABs A and B are not equivalent in quality with respect toparameter P. An equivalency index that falls between 98% and 90%, or ayellow zone, usually calls for reviewing of the data and the procedure.

[0039] In step 117, the method requires a repeat of steps 102 to 106 forthe remaining identified parameters.

[0040] In step 118, one declares that in regarding the product beingtested, FABs A and B are equivalent in quality when the equivalencyindices of the pre-identified set of parameters are all in the passingrange.

[0041]FIG. 2 depicts another embodiment of the invention, a method fordetermining whether a process in a semiconductor IC fabrication facility(FAB F) is equivalent in quality to a baseline process of anotherfacility (LAB L) based on Equivalency Indices. The method is similar inmany aspects to the method of FIG. 1. The main difference is that withthis method, one compares a facility of unknown quality to a baselineprocess of known quality. A laboratory is used in this embodiment toprovide the baseline process but the method applies equally well whenthe baseline of known quality is from an established manufacturingplant, or from results of computer simulation.

[0042] As with the method in FIG. 1, the generation of an equivalencyindex requires an integration operation, performed either manually orthrough a machine. Because the comparison is against a baseline of knownquality, the limits of integration will be chosen to be the 3-sigmapoints of the baseline. If the products under test have a smallerstandard deviation than that of the baseline process, it is possible forthe equivalency index of the facility under test to be greater than100%.

[0043] In step 201, the method requires one to identify one or morevariable parameters that are characteristic of the IC manufacturingprocess and that can be measured from a product manufactured with theprocess. The number of parameters that are necessary to make thisequivalency determination may be large or small, depending on thecomplexity of the process and the economy of the operation. In modernsemiconductor integrated circuit products, one may choose amongparameters related to a typical transistor in the integrated circuit,such as the transistor channel length, the gate oxide thickness, thedrive current, gate to substrate leakage current etc.

[0044] In step 202, one takes measurements of an identified parameter instep 201, for instance, the transistor drive current from a group of ICproducts manufactured in a first facility. FAB F. The measurement mayrequire hand probing by an operator if the desired sample size is small.Otherwise, it may require an automated system that incorporatesautomated testing system or data acquisition and computer system fordata crunching.

[0045] In step 203, one records the data from the measurements. Again,depending on the sample size, the recording may be in a laboratorynotebook, a personal computer, or a fully automated system.

[0046] In step 204, one constructs a probability distribution curve fromthe data recorded in step 203. Element 601 of FIG. 6 depicts such adistribution curve. Depending on the nature of the parameter, the datamay form different types of distribution. The most common distributionis the normal distribution or the bell-curve distribution. Other typesof distribution encountered in a typical manufacturing process includebinomial, chi-square, t, F, exponential, gamma, Pascal, Poisson andWeibull distribution. The method described here works well with normaland other types of discrete and continuous distributions. In case thedistribution does not conform to a commonly recognizable model, a personskilled in the art of statistical quality control will be able to usenumerical method or graphical method in implementing the teachingdisclosed in this invention.

[0047] In step 205, one extracts the average and the standard deviationfrom the probability distribution. The extraction may be accomplishedmanually or by a computer. It is familiar to a person skilled in the artof statistical quality control.

[0048] In step 206, one provides the baseline process information. Thebaseline may be from a batch of prototype product fabricated in alaboratory as in this example. It may be information gathered from aproduction run of an established factory or it may be from computersimulation. What is required of the baseline process is a distributioncurve with associated average and standard deviation against which thefacility under test will be compared. A baseline distribution curve isdepicted as element 601 in FIG. 6.

[0049] In step 207 one performs the integration of the distributioncurve generated in step 204 and depicted as element 602 in FIG. 6. Notethat the limits of integration C, element 611, and D, element 612 inFIG. 6 are the 3-sigma points of curve 601 of the baseline. Theintegration operation is usually performed by a machine. In simplecases, it may be performed manually.

[0050] In a mathematical form the integration may be written as

Ep=(∫ _(C) ^(D) f _(p)(x)dx)/99.7%,

[0051] where E_(p) is the equivalent index of parameter P of FAB F, Cand D are the 3-sigma points 611 and 612 of the probability distributioncurve 601 in FIG. 6, f_(p)(x) is the probability distribution function602 in FIG. 6. 99.7% is a weighing factor that will be discussed in step208.

[0052] In step 208, one normalizes the result of the integration. Inthis example, one uses a weighing factor of 99.7%. If the distributionunder test matches the distribution of the baseline perfectly, thenormalization would yield an number of 100%. The choice of 99.7% is aconvenient one and it is consistent with the custom of currentsemiconductor industry practice. One may choose a weighing factor otherthan 99.7% or omit the normalization step without deviating from theteaching of this method.

[0053] In step 209, this number is defined as the equivalency index ofthe parameter under test.

[0054] In step 210, one sets the thresholds to delineate the ranges ofpassing and failing of an equivalent index. In this example, passing isset at 98% and failing is set at 90%.

[0055] These particular threshold values are chosen because according tothe current semiconductor industry practice, when two probability curvesplotting data generated form two groups of products, are within onesigma shift distant apart, the two groups of products are considered asnot statistically significantly different from each other. If, however,the distance is more than a two-sigma shift, the two groups areconsidered to be significantly different. The threshold value of 98%, asshown in FIG. 5, conveniently corresponds to a one-sigma shift and thevalue of 90% is very closely corresponding to a two-sigma shift betweenthe two probability distribution curves.

[0056] While there is a statistical base for choosing these thresholdvalues, the method disclosed in this invention is equally effective withother choice of the threshold values based on other considerations suchas custom or economy. Also, this step may be performed temporallyindependent of other steps in the method. If the some considerationapplies for all the identified parameters under consideration, the sameset of threshold values may be used. Otherwise, one may choose to usedifferent threshold values for different parameters.

[0057]FIG. 5 depicts the relationship between values of an equivalencyindex and the corresponding shift of two probability distribution curvesthat generate the equivalency index. Element 501 depicts the scale ofequivalency indices and element 502 depicts the scale of thecorresponding shift.

[0058] In step 211, one compares the equivalency index E_(P) to theranges set in step 210. If E_(P) is in the range above the upperthreshold value of 98%, the passing range or a green zone, one woulddeclare that FAB F is equivalent in quality to LAB L with respect toparameter P. On the other hand, if E_(P) is in the range below the lowerthreshold value of 90%, a failing range or a red zone, one would declarethat FAB F is not equivalent in quality to LAB L with respect toparameter P. An equivalency index that falls between 98% and 90%, or ayellow zone, usually calls for reviewing of the data and the procedure.

[0059] In step 212, the method requires one to repeat steps 201 to 211for the remaining identified parameters.

[0060] In step 213, one declares that in regarding the product beingtested, FAB F and LAB L are equivalent in quality when the equivalencyindices of the pre-determined set of parameters all are in the passingrange.

[0061]FIG. 3 depicts yet another embodiment of the invention, a methodfor determining, with respect to one particular manufacturing processthat has been installed in a group of manufacturing facilities (FABs A,B, and C), which FABs are producing products that are equivalent inquality. The method is similar in many aspects as the method depicted inFIG. 1 and FIG. 2. In particular, like the method of FIG. 1, it does notrequire a baseline distribution except it does require a baseline targetvalue for the parameter. But unlike the method of FIG. 1, it compares aplurality of facilities instead of two facilities. Like the method inFIG. 2, the integration limits are picked from one particularprobability distribution instead of a combination of distributions.

[0062] In step 301, the method requires one to identify one or morevariable parameters that are characteristic of the IC manufacturingprocess and that can be measured from a product manufactured with theprocess. The number of parameters that are necessary to make thisequivalency determination may be large or small, depending on thecomplexity of the process and the economy of the operation. In modemsemiconductor integrated circuit products, one may choose amongparameters related to a typical transistor in the integrated circuit,such as the transistor channel length, the gate oxide thickness, thedrive current, gate to substrate leakage current etc.

[0063] In step 302, one takes measurements of an identified parameter instep 301, for instance, the transistor drive current from a group of ICproducts manufactured in a first facility. FAB A. The measurement mayrequire hand probing by an operator if the desired sample size is small.Otherwise, it may require an automated system that incorporatesautomated testing system for data acquisition and computer system fordata crunching.

[0064] In step 303, one records the data from the measurements. Again,depending on the sample size, the recording may be in a laboratorynotebook, a personal computer, or a fully automated system.

[0065] In step 304, one constructs a probability distribution curve fromthe data recorded in step 303. Element 701 of FIG. 7 depicts such adistribution curve. Depending on the nature of the parameter, the datamay form different types of distribution. The most common distributionis the normal distribution or the bell-curve distribution. Other typesof distribution encountered in a typical manufacturing process includebinomial, chi-square, t, F, exponential, gamma, Pascal, Poisson andWeibull distribution. The method described here works well with normaland other types of discrete and continuous distributions. In case thedistribution does not conform to a commonly recognizable model, a personskilled in the art of statistical quality control will be able to usenumerical method or graphical method in implementing the teachingdisclosed in -his invention.

[0066] In step 305, one extracts the average and the standard deviationfrom the probability distribution. The extraction may be accomplishedmanually or by a computer. It is familiar to a person skilled in the artof statistical quality control.

[0067] In step 306, one repeats the steps 302 to 305 on products fromFABs B and C.

[0068] In step 307, one compares the distributions of FABs A, B, and Cto determine on one FAB of which the measured data have the smalleststandard deviation. This sets the standard of variation against whichall facilities will be judged. If, however, due to other considerationsuch as cost, an alternative standard is more desirable, the choice ofsuch standard would not diminish the effectiveness of this method.

[0069] In step 311 one performs the integration of the distributioncurves generated in step 304 and depicted as element 701 in FIG. 7. Notethat the limits of integration C, element 711 and D, element 712 in FIG.7 are related to the 3-sigma points of curve 701 that has the smalleststandard deviation. The same limits C and D will be used in theintegration of all other probability distribution functions of otherFABs. The lower limit C, element 711 is set at

C=T−3×Sigma_(MIN);

D=T+3×Sigma_(MIN),

[0070] where C is the lower limit of the integration 711, T is thetarget value for parameter P 713, Sigma_(MIN) is the standard deviationof curve 701, and D is the upper limit of the integration, 712.

[0071] The integration operation is usually performed by a machine. Insimple cases, it may be performed manually.

[0072] In a mathematical form the integration may be written as

Epa=(∫_(C) ^(D) [f _(A)(x)]dx)/99.7%,

[0073] where E_(pa) is the equivalent index of parameter P of FAB A,f_(A)(x) is the probability distribution function 701, in FIG. 7 and99.7% is the weighing factor and will be explained in step 312.

[0074] In step 312, a division by a weighing factor of 99.7% normalizesthe result of the integration to yield a number between 100% and lessthan 1%. The purpose of the normalization is for the ease of automation.Choice of other weighing factors is also possible. Otherwise, thenormalization may also be omitted.

[0075] In step 313, one designates the result of the integration and thenormalization E_(PA) as the equivalent index for parameter P of the FABA under test.

[0076] In step 314, one sets the thresholds to delineate the ranges ofpassing and failing of an equivalent index. In this example, passing isset at 98% and failing is set at 90%. These particular threshold valuesare chosen because according to the current semiconductor industrypractice, when two probability curves plotting data generated form twogroups of products, are within one sigma shift distant apart, the twogroups of products are considered as not statistically significantlydifferent from each other. If, however, the distance is more than atwo-sigma shift, the two groups are considered to be significantlydifferent. The threshold value of 98%, as shown in FIG. 5, convenientlycorresponds to a one-sigma shift and the value of 90% is very closelycorresponding to a two-sigma shift between the two probabilitydistribution curves.

[0077] While there is a statistical base for choosing these thresholdvalues, the method disclosed in this invention is equally effective withother choice of the threshold values based on other considerations suchas custom or economy. Also, this step may be performed temporallyindependent of other steps in the method. If the some considerationapplies for all the identified parameters under consideration, the sameset of threshold values may be used. Otherwise, one may choose to usedifferent threshold values for different parameters.

[0078]FIG. 5 depicts the relationship between values of an equivalencyindex and the corresponding shift of two probabilty distribution curvesthat generate the equivalency index. Element 501 depicts the scale ofequivalency indices and element 502 depicts the scale of thecorresponding shift.

[0079] In step 315, one compares the equivalency index E_(PA) to theranges set in step 314. If E_(PA) is in the range above the upperthreshold value of 98%, the passing range or a green zone, one woulddeclare that FAB A has achieved a satisfactory equivalency in qualitywith respect to parameter P. On the other hand, if E_(PA) is in therange below the lower threshold value of 90%. a failing range or a redzone, one would declare that FAB A has not achieved such quality withrespect to parameter P. An equivalency index that falls between 98% and90%, or a yellow zone, usually calls for reviewing of the data and theprocedure.

[0080] In step 321, one repeats the steps 302 to 315 for all remainingidentified parameters.

[0081] In step 322, one declares that the FAB A has achieved theequivalency in quality with respect to the process under test and thequality is acceptable for the production of the product under test ifall parameters from FAB A are in the green zone set in step 314.

[0082] In step 323, one repeats step 311 to 322 for all other FABs. AnyFAB that has all its equivalency indices above the passing thresholdvalues or in the green zone would be grouped among the FABs that wouldbe qualified for the production of the product tested.

[0083] The disclosures and the description herein are purelyillustrative and are not intended to be in any sense limiting. A personskilled in the art of statistical quality control would be able to applythe method disclosed in the above embodiments to his or her particularproduct. The product may be goods or services and the product may be theprocess itself.

1. A method for qualifying a first product based on an equivalency indexassociated with a characteristic parameter of the product, comprising:a. identifying at least one variable characteristic parameter of thefirst product; b. measuring said parameter on a group of the firstproduct; c. recording the data of the measurement; d. constructing afirst probability distribution from the data; e. repeat step b and c ona group of a second product, the second product being possessive ofknown desirable quality; f. deriving an second average value and asecond standard deviation from the data taken from the second product;g. performing an integration of first probability distribution overlimits related to the second average values and second standarddeviations; h. deriving an equivalency index of said variablecharacteristic parameter based on the result of the integration; i.setting a threshold value for the equivalency index; j. comparing theequivalency index to the set threshold value; k. declaring the firstproduct as being of equivalent quality as the second product when theequivalency index of at least one identified characteristic parameter isnot lower than the set threshold value.
 2. The method of claim 1 whereinthe product is a goods of manufacture.
 3. The method of claim 1 whereinthe product is a service.
 4. A method for qualifying a first processbased on an equivalency index associated with a characteristic parameterof a product, the product being manufactured with the first process,comprising: a. identifying at least one variable characteristicparameter of a product manufactured with the first process; b. measuringsaid parameter on a first group of products manufactured with the firstprocess; c. recording the data of the measurement; d. constructing afirst probability distribution from the data; e. repeat step b and c ona second group of products, the second group of products beingmanufactured with a second process and the second process being of knowndesirable quality; f. deriving an second average value and a secondstandard deviation from the data taken from the second group ofproducts; g. performing an integration of first probability distributionover limits related to the second average values and the second standarddeviations; h. deriving an equivalency index of said variablecharacteristic parameter based on the result of the integration; i.setting a threshold value for the equivalency index; j. comparing theequivalency index to the set threshold value; k. declaring the firstprocess as being of equivalent quality as the second process when theequivalency index of at least one identified characteristic parameter isnot lower than the set threshold value.
 5. The method of claim 4 whereinthe process is for manufacturing a semiconductor integrated circuit. 6.The method in claim 4 wherein the product is a semiconductor integratedcircuit.
 7. (cancelled).
 8. A method for qualifying a product based onan equivalency index associated with a characteristic parameter of thefirst product, comprising: a. identifying at least one variablecharacteristic parameter of the product; b. measuring said parameter ona group of the products; c. recording the data of the measurement; d.constructing a first probability distribution from the data; e.providing a desired target average value and a desired standarddeviation value; f. performing an integration of the first probabilitydistribution over limits related to the desired target average value andthe desired standard deviation value; g. deriving an equivalency indexof said variable characteristic parameter based on the result of theintegration; h. setting a threshold value for the equivalency index; i.comparing the equivalency index to the set threshold value; j. declaringthe product as being of quality meeting the average and standarddeviation targets when the equivalency index of at least one identifiedcharacteristic parameter is not lower than the set threshold value. 9.The method in claim 8 wherein the product is a goods of manufacture. 10.The method in claim 8 wherein the product is a service.
 11. A method forqualifying a first process based on an equivalency index associated witha characteristic parameter of a product, the product being manufacturedwith the first process, comprising: a. identifying at least one variablecharacteristic parameter of a product manufactured with said process; b.measuring said parameter on a first group of products manufactured withsaid process; c. recording the data of the measurement; d. constructinga first probability distribution from the data of the measurements; e.providing a desired target average value and a desired standarddeviation value; f. performing an integration of the first probabilitydistribution over limits related to the desired target average value andthe desired standard deviation value; g. deriving an equivalency indexof said variable characteristic parameter based on the result of theintegration; h. setting a threshold value for the equivalency index; i.comparing the equivalency index to the set threshold value; j. declaringthe first process as being of quality meeting the average and standarddeviation targets when the equivalency index of at least one identifiedcharacteristic parameter is not lower than the set threshold value. 12.The method in claim 11 wherein the process is a process formanufacturing a semiconductor integrated circuit.
 13. The method inclaim 11 wherein the product is a semiconductor integrated circuit. 14.(cancelled).
 15. A method for declaring two products, a first productand a second product, as being equal, based on an equivalency indexassociated with a characteristic parameter common to the two products,comprising: a. identifying at least one variable characteristicparameter common to the two products; b. measuring said parameter on agroup of the first product; c. recording the data of the measurement; d.constructing a first probability distribution from the data; e.determining a first average value and a first standard deviation of saidfirst probability distribution; f. repeating steps b through c with agroup of the second product; g. constructing a second probabilitydistribution from the data of measurements taken from the group of thesecond product; h. determining an second average value and a secondstandard deviation of the second probability distribution; i. performingan integration of the sum of the two probability distributions overlimits related to the first and second average values and the first andsecond standard deviations; j. deriving an equivalency index of saidvariable characteristic parameter based on the result of theintegration; k. setting a threshold value for the equivalency index; l.comparing the equivalency index to the set threshold value; m. declaringsaid two products as being equivalent in quality when the equivalencyindex of at least one identified characteristic parameter is not lowerthan the set threshold.
 16. The method in claim 15 wherein the twoproducts are goods of manufacture.
 17. The method in claim 15 whereinthe two products are services.
 18. A method for declaring two processes,a first process and a second process, as being equal, based on anequivalency index associated with a characteristic parameter to aproduct manufactured with the two processes, comprising: a. identifyingat least one variable characteristic parameter of the product, theproduct being manufactured with the two processes; b. measuring saidparameter on a first group of the product, the first group of theproduct being manufactured with the first process; c. recording the dataof the measurement; d. constructing a first probability distributionfrom the data in step c; e. determining a first average value and afirst standard deviation of said first probability distribution; f.repeating steps b and c on a second group of the product, the secondgroup of the product being manufactured with a second process; g.constructing a second probability distribution from the data taken fromthe second group of product; h. determining an second average value anda second standard deviation of said second probability distribution; i.performing an integration of the sum of the two probabilitydistributions over limits related to the first and second average valuesand the first and second standard deviations; j. deriving an equivalencyindex of said variable characteristic parameter based on the result ofthe integration; k. setting a threshold value for the equivalency index;l. comparing the equivalency index to the set threshold value; m.declaring said two facilities as possessive of said process ofequivalent quality when the equivalency index of at least one identifiedcharacteristic parameter is not lower than the set threshold.
 19. Themethod of claim 18 wherein the two processes are for manufacturing asemiconductor integrated circuit.
 20. The method of claim 18 wherein theproduct is a semiconductor integrated circuit.
 21. (cancelled)
 22. Amethod for declaring a plurality of products as being equivalent inquality, based on an equivalency index associated with a characteristicparameter common to the plurality of products, comprising: a.identifying at least one variable characteristic parameter common to theplurality of products; b. measuring said parameter on a group of a firstproduct of the plurality of products; c. recording data of themeasurement; d. constructing a first probability distribution from thedata; e. determining a first standard deviation of said firstprobability distribution; f. repeating steps b and c on a group of asecond product of the plurality of products; g. constructing a secondprobability distribution from the data; h. determining a second standarddeviation of said second probability distribution; i. repeating steps fand g for the remaining of the plurality of products; j. providing adesired target value for said parameter; k. integrating the firstprobability distribution over a pair of limits, the pair of limits beingrelated to the desired target value; l. deriving an equivalency index ofsaid variable characteristic parameter based on the result of theintegration; m. setting a threshold value for the equivalency index; n.comparing the equivalency index to the set threshold value; o. repeatingsteps k, l, and n for each of the remaining plurality of products; p.declaring each of the plurality of products as having achieved theequivalency in quality and the quality being satisfactory when at leastone equivalency index associated with the each of the plurality ofproducts is not lower than the set threshold value.
 23. The method ofclaim 22 wherein the plurality of products are products of manufacture.24. The method of claim 22 wherein the plurality of products areservices.
 25. A method for declaring a plurality of processes as beingequivalent in quality based on an equivalency index associated with acharacteristic parameter of a product manufactured with said processes,comprising: a. identifying at least one variable characteristicparameter of the product manufactured with said processes; b. measuringsaid parameter on a first group of products, the products beingmanufactured with a first process of the plurality of processes; c.recording data of the measurement; d. constructing a first probabilitydistribution from the data; e. determining a first standard deviation ofsaid first probability distribution; f. repeating steps b and c on asecond group of products, the second group of products beingmanufactured with a second process of the plurality of processes; g.constructing a second probability distribution from the data; h.determining a second standard deviation of said second probabilitydistribution; i. repeating steps f through h for the remaining of theplurality of processes; j. providing a desired target value for saidparameter; k. integrating the first probability distribution over a pairof limits, the pair of limits being related to the desired target value;l. deriving an equivalency index of said variable characteristicparameter based on the result of the integration; m. setting a thresholdvalue for the equivalency index; n. comparing the equivalency index tothe set threshold value; o. repeating steps k, l, and n for each of theremaining plurality of processes; p. declaring each of the plurality ofprocesses as having achieved the equivalency in quality and the qualitybeing satisfactory when at least one equivalency index associated withthe each of the plurality of processes is not lower than the setthreshold value.
 26. The method in claim 25 wherein the plurality ofprocesses are for making semiconductor integrated circuits.
 27. Themethod of claim 25 wherein the product is a semiconductor integratedcircuit.
 28. (cancelled).